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- W2802158394 abstract "We introduce the emph{Online Connected Dominating Set Leasing} problem (OCDSL) in which we are given an undirected connected graph $G = (V, E)$, a set $mathcal{L}$ of lease types each characterized by a duration and cost, and a sequence of subsets of $V$ arriving over time. A node can be leased using lease type $l$ for cost $c_l$ and remains active for time $d_l$. The adversary gives in each step $t$ a subset of nodes that need to be dominated by a connected subgraph consisting of nodes active at time $t$. The goal is to minimize the total leasing costs. OCDSL contains the emph{Parking Permit Problem}~cite{PPP} as a special subcase and generalizes the classical offline emph{Connected Dominating Set} problem~cite{Guha1998}. It has an $Omega(log ^2 n + log |mathcal{L}|)$ randomized lower bound resulting from lower bounds for the emph{Parking Permit Problem} and the emph{Online Set Cover} problem~cite{Alon:2003:OSC:780542.780558,Korman}, where $|mathcal{L}|$ is the number of available lease types and $n$ is the number of nodes in the input graph. We give a randomized $mathcal{O}(log ^2 n + log |mathcal{L}| log n)$-competitive algorithm for OCDSL. We also give a deterministic algorithm for a variant of OCDSL in which the dominating subgraph need not be connected, the emph{Online Dominating Set Leasing} problem. The latter is based on a simple primal-dual approach and has an $mathcal{O}(|mathcal{L}| cdot Delta)$-competitive ratio, where $Delta$ is the maximum degree of the input graph." @default.
- W2802158394 created "2018-05-17" @default.
- W2802158394 creator A5081533618 @default.
- W2802158394 date "2018-05-07" @default.
- W2802158394 modified "2023-09-27" @default.
- W2802158394 title "Online Connected Dominating Set Leasing" @default.
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